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Analytic measures and Bochner measurability
Let be a -algebra over , and let denote
the Banach space of complex measures. Consider a representation for
acting on . We show that under certain, very weak
hypotheses, that if for a given and all the
map is in , then it follows that the
map is Bochner measurable. The proof is based upon the idea
of the Analytic Radon Nikod\'ym Property.
Straightforward applications yield a new and simpler proof of Forelli's main
result concerning analytic measures ({\it Analytic and quasi-invariant
measures}, Acta Math., {\bf 118} (1967), 33--59)
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